Question

What is the true weight of an object in a geostationary satellite that weighed exactly 10.0 N at the north pole?

Answer 1

For a geostationary satellite, we have:
R = 6.4 × 10³ km
h = 3.6 × 10³ km
Given: mg = 10 N

The true weight of the object in the geostationary satellite is given by
$$\begin{gathered} mg\text{'}=mg-\frac{R^2}{{\left(R+h\right)}^2} \\ =10-\frac{{\left(6400\times {10}^3\right)}^2}{\left(6400\times {10}^3+3600\times {10}^3\right)} \\ =10-\left[\frac{{\left(64\times {10}^5\right)}^2}{\left(6.4\times {10}^6+36\times {10}^5\right)}\right] \\ =10-\left[\frac{4096\times {10}^{10}}{{\left(42.4\right)}^2\times {10}^{12}}\right] \\ =\frac{4096}{17980}=0.227\mathrm{N} \end{gathered}$$